A major problem in the genetic epidemiology of familial diseases and traits associated with diseases, concerns the derivation of biologically realistic and computationally practical models that account for major genes as well as covariates, and less specific sources of familial covariation such as common environment, cultural transmission, and other factors with separately indistinguishable effects. The older approach, the mixed model and its derivatives, specifies major gene effects, and partitions the residual variance into polygenic and environmental components. This model explains familial correlations essentially in terms of genetic causation. Regressive models, on the other hand, are constructed by successively conditioning on major genotypes, phenotypes antecedents, and other covariates. Familial patterns of dependence, which include that underlying the mixed model, are described in terms of correlations without necessarily introducing a particular scheme of causal relationships. Regressive models provide a practical approach to the modeling problem. Simulation studies are proposed to establish the numerical equivalence of the mixed and regressive models; to delineate the properties of the regressive models as comprehensive models in the epidemiology and genetics of familial diseases and other traits. The simulations, which have been started for segregation analysis of continuous traits assuming simple patterns of familial correlations, will be extended to discrete traits and more complex situations, including assortative mating, common family environment, unequal mother- child, father-child and within sibship correlations, and deviations from normality assumptions for continuous traits. In addition, the usefulness of incorporating residual correlations as specified by the regressive models, into linkage analysis, will be evaluated.